论文标题
年龄结构化模型具有迪里奇类型的非局部扩散，I：主要光谱理论和限制特性
Age-structured Models with Nonlocal Diffusion of Dirichlet Type, I: Principal Spectral Theory and Limiting Properties
论文作者
论文摘要
具有非本地扩散的年龄结构化模型自然出现在描述生物物种的种群动力学以及传染病的传播动力学，其中个体非局部分散并相互相互作用，并且个人的年龄结构很重要。在我们的系列论文的第一部分中，我们研究了具有Dirichlet类型非本地扩散的年龄结构化模型的主要光谱理论。首先，我们通过使用解决方案的阳性操作者的理论来提供有关主要特征值的两个标准。然后，我们定义了广义的主特征值，并使用它来研究扩散速率对主特征值的影响。此外，我们为年龄结构的非本地扩散算子建立了强大的最大原理。在第二部分\ cite {ducrot2022age-age-age-age-Losenturedii}我们将研究主要特征值对模型的全球动态的影响，其出生率单调非线性，并表明主要特征值是Zero的。
Age-structured models with nonlocal diffusion arise naturally in describing the population dynamics of biological species and the transmission dynamics of infectious diseases in which individuals disperse nonlocally and interact each other and the age structure of individuals matters. In the first part of our series papers, we study the principal spectral theory of age-structured models with nonlocal diffusion of Dirichlet type. First, we provide two criteria on the existence of principal eigenvalues by using the theory of resolvent positive operators with their perturbations. Then we define the generalized principal eigenvalue and use it to investigate the influence of diffusion rate on the principal eigenvalue. In addition, we establish the strong maximum principle for age-structured nonlocal diffusion operators. In the second part \cite{Ducrot2022Age-structuredII} we will investigate the effects of principal eigenvalues on the global dynamics of the model with monotone nonlinearity in the birth rate and show that the principal eigenvalue being zero is critical.
